Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Let G be a semi-simple algebraic group over a field k. Projective G-homogeneous varieties are projective varieties over which G acts transitively. The stabilizer or the isotropy subgroup at a point on such a variety is a parabolic subgroup which is always smooth when the characteristic of k is zero. However, when k has positive characteristic, we encounter projective varieties with transitive G-action where the isotropy subgroup need not be smooth. We call these varieties projective pseudo-homogeneous varieties. To every such variety, we can associate a corresponding projective homogeneous variety. In this thesis, we extensively study the Chow motives (with coefficients from a finite connected ring) of projective pseudo-homogeneous varieties for G inner type over k and compare them to the Chow motives of the corresponding projective homogeneous varieties. This is done by proving a generic criterion for the motive of a variety to be isomorphic to the motive of a projective homogeneous variety which works for any characteristic of k. As a corollary, we give some applications and examples of Chow motives that exhibit an interesting phenomenon. We also show that the motives of projective pseudo-homogeneous varieties satisfy properties such as Rost Nilpotence and Krull-Schmidt.

Incorporating grape seed antioxidants into a functional food model

Gemstone Team IMMUNE (Innovative Medicines for Maladies Utilizing Nutraceutical Enhancements)

PIANIST-COMPOSERS WHOSE WORKS INCLUDE PIANISTIC INNOVATIONS

Throughout the piano’s history, certain composers have created innovations in the areas of virtuosity and sonority. These innovations came not only from the composers’ imagination, but also from the development of instruments and changes in musical style from one period to another. To investigate what kinds of innovations these pianist composers made, I divided them into technique and sound from Mozart to Cowell. I chose two-piano music (Sonata in D major, K.448 by Mozart and Rachmaninoff’s Second Suite) to demonstrate their experiments with varieties of textures and sonorities, using different registers of the two pianos orchestrally. En Blanc et noir by Debussy shows this composer’s deep interest and originality in piano sonorities. For solo piano music, Beethoven’s Piano Sonata Op.53 shows extensive technical invention. His use of long pedal effects shows a pianistic possibility not explored by Mozart. Hummel’s Piano Sonata in D major represents orchestral devices as well as pianistic techniques showing recent developments in the instrument. Chopin’s Ballade No.3 and Scherzo No.3 show virtuosic moments and also the expanded range of the keyboard. His Nocturne Op.27, no.2, with its sonorities resulting from the combination of pedal, and widespread accompaniments derived from Alberti bass figures, is a perfect example of Chopin’s characteristic sound-world. “Vallée d’Obermann” by Liszt uses many virtuosic techniques as well as the extreme wide ranges of keyboard in both hands to create dramatic contrasts of texture. Debussy’s etude, “Pour les Sonorités opposés” is probably the first etude designed for sonority rather than for keyboard virtuosity. Albeniz’s “Evocación” and “Triana” show Spanish atmosphere. Prokofiev’s Sonata no.3 shows frequent motoric driving elements that demand percussive virtuosity. Cowell’s piano music is some of the earliest to explore the sonorities of tone clusters and playing on the strings. This performance dissertation consists of three recitals performed in the Orchestra Room, Leah Smith Hall, and Gildenhorn Recital Hall at the University of Maryland, College Park. These recitals are documented on compact disc recordings that are housed within the University of Maryland Library System.

Polish Violin Music in the 20th and 21st Century

The purpose of this dissertation is to promote Polish violin music written in the 20th and 21st Century. My recitals included many lesser-known compositions and composers which I strongly believe deserve to be better known and more often performed. The search and preparation of those pieces, for which recordings and music scores are not easily found, was a very exciting and stimulating process. Much Polish music written in the 20th and 21st Century is interesting, expressive, beautiful, and deserves to be more often performed. Performing 20th and 21st Century music opens new perspectives in two directions: musically and technically. Performer and listener are, in many cases, unbound from tonality. Composers are looking for new sonorities and exploring such performing techniques as varieties of harmonics, quarter tones, extreme dynamics, complex rhythms, and usage of a wide range of registers. An important part of Polish music is Polish folklore. The little town of Zakopane is known for Polish traditional clothing, food, architecture, dance and music. Also, most prominent Polish luthiers including Wojciech Topa, whose instrument I am playing, have been making their instruments in Zakopane. This little town in the Tatras Mountain has been an inspiration for many Polish artists including Iwaszkiewicz, Witkacy, Karłowicz, and Szymanowski. Those composers used such folklore elements as folk scales, popular tunes, and imitations of the sound of the folk band with characteristic folk dance rhythms. Other musical genres where folk elements are strongly present are the compositions dedicated to young musicians, with a specifically educational purpose. Among composers who wrote educational music were Grażyna Bacewicz, Witold Lutosławski, and Henryk Mikołaj Górecki. This approach makes the works more easily understood by young performers and, at the same time, broadens their understanding of Polish culture and prepares them for the challenges of contemporary music. This has been an exciting project for me because, on the one hand, it allowed me the challenge of performing compositions that are lesser-known and often consist of musical language new to me while, on the other, it brought me back to my roots and the country of my mother tongue.